Empirical Predictions of Seafloor Properties Based on Remotely Measured Sediment

Impedance

Michael D. Richardson and Kevin B. Briggs

Marine Geosciences Division, Naval Research Laboratory, Stennis Space Center MS 39529-5004

Abstract. Numerous acoustic systems have been developed over the past 25 years for remote classification of the seabed. Many systems use inversions of echo returns to estimate seafloor impedance and then use empirical relationships to predict other seabed properties from values of impedance. New regressions are presented, separately for siliciclastic and carbonate sediments, which allow prediction of sediment grain size, porosity, bulk density, percent sand and gravel and sound speed ratio and attenuation from values of an index of impedance (product of sound speed ratio and bulk density). This index is independent of pore water temperature and salinity and water depth. The regressions are based on nearly 800 cores collected from 67 shallow-water sites around the world (12 carbonate and 55 siliciclastic sites). Data are typically restricted to the upper 30 cm of sediment. The regressions based on the nearly 4,500 common data points from core measurements (3,922 for siliciclastic and 621 for carbonate sediments) do not vary significantly from the regressions for siliciclastic sediments first presented by Richardson and Briggs (1993) or between carbonate and siliciclastic sediments suggesting the empirical predictions universally apply to coastal sediments. Sound speed dispersion, sediment disturbance during core collection and measurement, inequalities between sample size (acoustic footprint vs. core diameter), spatial variability, and regression error all affect the accuracy of sediment property predictions.

INTRODUCTION

Many acoustic sediment classification systems use the amplitude of echo returns to estimate seafloor impedance. Empirical relationships between seafloor impedance and sediment physical properties are then used to map seafloor physical properties such porosity, bulk density, percent sand and gravel, or mean grain size and geoacoustic properties such as sound speed and attenuation. In this paper, we provide an update to the empirical relationships first given by Richardson and Briggs [1] to predict values of seafloor properties from a temperature-independent index of acoustic impedance. In the 1993 paper, the authors analyzed 1,243 measurements of impedance and physical properties from 211 cores collected from 22 sediment types at 11 siliciclastic sites. For this paper the data set has been expanded to over 4,500 measurements from 67 shallow water sites, with both siliciclastic and carbonate sediments represented (Tables 1 and 2). Our first objective is to determine if the almost-5-times-larger data set collected over a wider range of sediment types yields differences in empirical relationships between an index of impedance and related sediment physical and geoacoustic properties. The second objective is to determine whether these empirical regressions

yield different predictions from carbonate and siliciclastic sites as suggested by Richardson and colleagues from the analyses of sediments collected from the Florida Keys [2].

METHODS FOR SEDIMENT COLLECTION AND LABORATORY DATA ANALYSES

Sediment geoacoustic and physical property measurements were made from sediments collected with 45-cm-long, 5.9-cm-inside-diameter, clear, polycarbonate coring tubes. Most sediments were collected by divers but sediments collected from eight sites (Montauk Point, Quinault Range, Arafura Sea, Russian River, Eel River, North Sea , TOSSEX, and Straits of Juan de Fuca), which were too deep for diving operations, were subsampled from 0.25m2 spade box cores. Cores were capped at both ends immediately after collection to retain the overlying water and kept in an upright position during transport to the laboratory for analysis. Collection, measurement, and handing procedures were designed to minimize sampling disturbance and to maintain an intact sediment-water interface within the coring tube.

Sound speed and attenuation were measured on sediment at 1-cm intervals within the core tubes, usually within 24 hours of collection, using time-of-flight and amplitude of pulsed 400-kHz sine waves transmitted across the core tube [3]. Sediment sound speed is calculated from the differences in time-of-flight between sediment and distilled water within identical core tubes, the measured inside diameter of the core tube (5.9 cm), and the sound speed within the distilled water. Attenuation is measured as 20 log of the ratio of the mean amplitude of the waveform transmitted through water to those transmitted through sediment. Sound speeds are reported as the unitless sound speed ratio (Vp ratio) which is the ratio of measured sound speed to the sound speed of pore water at the same temperature, salinity and pressure. Attenuation is expressed in units of dB m-1kHz-1 (k) after Hamilton [4].

Sediments were then extruded from sediment cores and sectioned at 2-cm intervals to determine sediment porosity and grain size distribution. Porosity was determined from weight loss of sediments dried at 105° C for 24 hours and corrected for residual salt. Grain density was determined using a pyncnometer. Sediment bulk density was calculated from the porosity and densities of pore water and sediment grains. Sediment grain size was determined from disaggregated samples by dry sieving for sand-sized particles and by either pipette methods or Micromeritics sedigraph for silt- and clay-sized particles.

Sediment impedance (Z, kg m-1s-1) is the product of sediment sound speed and bulk density. Sediment sound speed is dependent on pore water temperature and salinity and pressure (water depth). Furthermore, sound speed in sediment at a single site can vary up to 10% over the range of seasonal conditions expected in coastal waters [1]. Therefore, the pore-water-independent Index of Impedance (IOI), which is the product of the sediment bulk density and velocity ratio, is used to calculate empirical relationships between sediment impedance and other sediment physical properties.

RESULTS AND DISCUSSION

Sediment physical and geoacoustic properties were measured on over 800 cores collected from 67 shallow-water sites around the world (12 carbonate and 55 siliciclastic sites). The total of 4,582 collocated measurements is nearly 5-times the number of measurements used by Richardson and Briggs [1] to determine similar empirical relationships between the index of impedance (IOI) and sediment physical and geoacoustic properties and includes measurements in carbonate sites (609) as well as siliciclastic sites (3973). Sediment at the 55 siliciclastic sites ranged from very-high-porosity clays (such as Eckernförde Bay, Baltic Sea or St. Andrew Bay, Florida) to coarse sands in the northeastern Gulf of Mexico (Table 2). Siliciclastic sampling sites were generally associated with high-frequency acoustic bottom scattering experiments and include sites in the Mediterranean, Baltic and North Seas, and along the entire range of Atlantic, Pacific and Gulf coasts of the US [1,3,5]. Carbonate sampling sites are geographically restricted to tropical waters along the southern coastline of Florida [2] and Hawaii but, nevertheless include several sediment types (Table 1).

The Index of Impedance (IOI) provides excellent predictions of sound speed ratio, bulk density, and porosity for both carbonate and siliciclastic sediments (Figures 1 and 2; Tables 3 and 4). This is not surprising as IOI is the product of velocity ratio (VpR) and bulk density, and both sediment bulk density and porosity are determined from the same wet loss measurements. Predictions of Vp, VpR, bulk density and porosity for carbonate and siliciclastic sediments vary less than 14 m s-1, 0.001, 0.04 g cm-3, 4% respectively, over the full range of values of IOI suggesting regressions for each parameter derived from the entire data set is appropriate (Table 5). The coefficients of determination (r2) between IOI and sediment mean grain size and percent sand and gravel are lower for carbonates than siliciclastic sediments. The lower values of r2

between IOI and grain size properties due to scatter in the data justify combined regressions using all carbonate and siliciclastic data in spite of up to 0.6 phi and 17% differences in predicted mean grain size and percent sand and gravel. Based on the data presented, attenuation is poorly predicted from impedance.

TABLE 1. Mean values of sediment physical and geoacoustic properties from carbonate sites located in southern Florida and in Hawaii. Sediment properties include sound speed (Vp, m s-1), sound speed ratio (VpR, no units), attenuation (α, dB m-1; k, α kHz-1), mean grain size (Mz, phi) porosity (η, %), density (ρ, g cm-3) and the Index of Impedance (IOI, g cm-3). Sites are ordered as increasing values of IOI.

Site Vp VpR Mz k IOI Sediment Hawaii/mud 1495.3 0.977 68.6 8.67 84.02 1.296 0.171 1.267 calc. silty clay MarqKeys 1555.6 1.017 391.3 6.15 59.66 1.726 0.978 1.755 calc. s-s-clay SG98-5 1560.8 1.020 322.3 5.85 59.59 1.748 0.806 1.783 calc. s-s-clay DTortugas 1561.8 1.021 343.0 6.62 59.00 1.755 0.858 1.792 calc. s-s-clay LFK/fine 1581.3 1.034 365.8 5.40 57.19 1.759 0.914 1.818 calc. s-s-clay Hawaii-4 1609.7 1.052 246.2 3.88 56.42 1.771 0.615 1.864 calc. silty sand SG98-2 1669.4 1.091 383.1 1.57 49.47 1.921 0.958 2.096 crse. skel. sand Hawaii/crse 1639.4 1.072 695.2 0.74 45.18 1.960 1.738 2.100 crse. coral sand Hawaii-2 1671.6 1.093 438.3 2.33 47.68 1.933 1.096 2.112 calc. med. sand LFK/crse 1704.7 1.114 488.9 0.54 41.97 2.054 1.222 2.289 crse. coral sand RebShoal 1733.1 1.133 279.1 1.26 43.85 2.022 0.698 2.290 carbonate sand SG98-3 1777.3 1.162 236.7 1.66 40.92 2.067 0.592 2.401 ooid/skel. sand

TABLE 2. Mean values of sediment physical and geoacoustic properties from 55 siliciclastic sites world-wide. Sediment properties include sound speed (Vp, m s-1), sound speed ratio (VpR, no units), attenuation (α, dB m-1; k, α kHz-1), mean grain size (Mz, phi) porosity (η, %), density (ρ, g cm-3) and the Index of Impedance (IOI, g cm-3). Sites are ordered as increasing values of IOI.

Site Vp VpR Mz k IOI Sediment Type SABay 1518.9 0.993 38.7 10.94 89.14 1.170 0.097 1.162 clay Eck93 1515.5 0.991 72.3 9.88 87.40 1.188 0.181 1.177 silty clay CLBight 1521.9 0.995 114.0 8.10 86.50 1.223 0.285 1.216 silty clay JDF7 1507.2 0.985 114.2 8.50 83.43 1.313 0.285 1.294 silty clay LISound 1503.1 0.982 — 7.64 76.64 1.411 — 1.386 clayey silt Orcas 1511.9 0.988 179.1 8.08 75.22 1.403 0.448 1.387 clayey sand Diga 1480.4 0.968 58.0 10.05 69.12 1.506 0.145 1.458 silty clay JDF4 1521.7 0.995 206.8 6.93 74.35 1.470 0.517 1.462 glacial till Arafura 1511.4 0.988 347.8 5.24 71.63 1.494 0.869 1.476 clayey sand Portovenere 1501.7 0.982 66.2 9.45 68.30 1.546 0.166 1.518 silty clay STeresa 1502.4 0.982 122.3 8.78 66.98 1.569 0.306 1.541 silty clay RussRiver 1545.5 1.010 231.8 6.35 64.35 1.597 0.579 1.613 clayey sand Viareggio 1511.3 0.988 99.5 8.98 61.74 1.634 0.249 1.615 silty clay Eck94 1609.7 1.052 210.7 4.59 59.38 1.659 0.527 1.745 sand-silt-clay EelRiver 1554.6 1.016 190.7 7.17 57.32 1.745 0.477 1.773 clayey silt ATB/G40 1651.9 1.080 219.8 2.56 56.61 1.716 0.549 1.853 fine sand JDF1 1617.6 1.057 238.5 4.37 55.37 1.800 0.596 1.903 silty fine sand Tellaro 1614.4 1.055 184.7 6.08 50.70 1.820 0.462 1.921 sand-silt-clay Monasteroli 1652.4 1.080 220.2 5.12 46.62 1.891 0.550 2.042 sand-silt-clay JDF6 1668.2 1.090 314.3 2.94 47.56 1.922 0.786 2.096 fine sand/s-s-c Tirrenia 1683.1 1.100 127.6 3.72 45.76 1.906 0.319 2.097 v.fine sand VAzzura 1686.4 1.102 156.5 4.14 45.17 1.911 0.391 2.106 muddy sand SG98-6 1649.6 1.078 632.5 0.08 43.47 2.001 1.581 2.158 shell/coral hash JDF5 1701.5 1.112 213.8 2.31 45.44 1.946 0.534 2.164 fine sand/s-s-c LTB 1716.8 1.122 317.1 2.54 43.57 1.929 0.793 2.165 fine sand Quinault 1709.3 1.117 177.2 2.94 41.76 1.971 0.443 2.202 fine sand PC93 1708.5 1.117 404.0 0.98 40.93 2.008 1.010 2.242 coarse sand PCII 1716.4 1.122 391.2 0.85 41.09 2.000 0.978 2.244 c. sand/sh. hash TBay/crse 1754.2 1.147 610.2 1.36 44.85 1.966 1.526 2.254 coarse/fine sand KB/lyn 1709.2 1.117 586.9 0.90 40.14 2.020 1.467 2.256 shell hash Charl/fine 1728.4 1.130 281.0 1.97 39.94 2.001 0.703 2.260 fine sand SG98-10 1752.1 1.145 164.1 1.62 40.69 1.979 0.410 2.266 medium sand Charl/crse 1729.1 1.130 308.1 1.44 39.63 2.006 0.770 2.267 medium sand PC84 1742.9 1.139 241.7 2.61 40.08 1.998 0.604 2.276 fine sand SWEAT 1747.6 1.142 213.3 2.23 40.38 2.007 0.533 2.292 fine sand SG98-9 1747.1 1.142 206.7 1.56 39.45 2.010 0.517 2.295 medium sand TBay/fine 1746.0 1.141 206.1 2.92 40.16 2.013 0.515 2.297 fine sand ATB/B14 1752.6 1.146 107.2 2.15 39.52 2.006 0.268 2.298 fine sand SG98-1 1713.0 1.120 430.2 0.84 40.66 2.053 1.076 2.299 shell hash IRB 1745.2 1.141 281.2 1.77 40.63 2.023 0.703 2.307 medium sand SG98-8 1747.1 1.142 265.7 2.14 39.65 2.026 0.664 2.314 shelly fine sand PCB I&II 1755.1 1.147 176.1 2.34 39.72 2.018 0.440 2.315 fine sand NS 1735.0 1.134 226.1 1.87 41.07 2.046 0.565 2.320 medium sand MVCO 1755.1 1.147 154.5 2.52 38.49 2.028 0.386 2.327 fine sand PCB99 1764.2 1.153 133.5 2.24 39.33 2.020 0.334 2.329 fine sand MonPt 1744.4 1.140 92.1 2.04 37.21 2.045 0.230 2.332 fine sand KB/bar 1758.2 1.149 254.4 1.33 37.28 2.047 0.636 2.352 medium sand Duck 1758.8 1.150 116.2 2.53 39.54 2.051 0.291 2.357 fine sand JDF2 1771.6 1.158 179.5 2.03 39.10 2.039 0.449 2.361 medium sand PE99 1770.7 1.157 153.0 1.28 37.08 2.052 0.383 2.375 medium sand PE00 1774.1 1.160 149.5 1.21 37.32 2.050 0.374 2.377 medium sand SAX99 1766.3 1.154 177.5 1.27 37.27 2.066 0.444 2.385 medium sand NoSea 1779.0 1.163 155.7 1.93 37.56 2.054 0.390 2.388 med/fine sand TOSSEX 1762.7 1.152 161.8 1.93 35.64 2.075 0.404 2.391 med/fine sand HoodCanal 1767.1 1.155 184.6 1.34 36.46 2.108 0.462 2.435 medium sand

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FIGURE 1. Empirical relationships used to predict sediment physical and acoustic properties from the Index of Impedance (IOI) for carbonate sediments. Data and regressions (Table 1, Table 3) are based on 69 cores collected from 12 sites around southern Florida and in the Hawaiian Islands.

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FIGURE 2. Empirical relationships used to predict sediment physical and acoustic properties from the Index of Impedance (IOI) for siliciclastic sediments. Data and regressions (Table 2; Table 4) are based on over 3,900 measurements made on cores collected from 55 shallow-water sites world-wide.

TABLE 3. Empirical Predictive Relationships for Sediment Physical and Geoacoustic Properties Based on the Index of Impedance (IOI) for Carbonate Sediments. Coefficient of determination (r2) is given for each regression.

Parameter Regression r2 Sound Speed Ratio = 1.164 - 0.3001(IOI) + 0.1253(IOI)2 0.96Attenuation (k) = -5.96 + 6.94(IOI) � 1.174(IOI)2 0.43Porosity (%) = 186.18 � 102.20(IOI) + 17.29(IOI)2 0.99Density (g cm-3) = -0.52 + 1.81(IOI) � 0.305(IOI)2 0.99Mean Grain Size (θ) = 19.3 -7.6(IOI) 0.75Sand and Gravel (%) = -143.2 + 101.4(IOI) 0.73

TABLE 4. Empirical Predictive Relationships for Sediment Physical and Geoacoustic Properties Based on the Index of Impedance (IOI) for Siliciclastic Sediments. Coefficient of determination (r2) is given for each regression.

Parameter Regression r2 Sound Speed Ratio = 1.149 - 0.2821(IOI) + 0.1203(IOI)2 0.97Attenuation (k) = -2.61 + 3.41(IOI) � 0.885(IOI)2 0.16Porosity (%) = 178.60 � 94.60(IOI) + 14.86 (IOI)2 0.99Density (g cm-3) = 1.01 + 1.22LN(IOI) 0.99Mean Grain Size (θ) = 17.7 -6.8(IOI) 0.85Sand and Gravel (%) = -109.6 + 87.7(IOI) 0.82

TABLE 5. Empirical Predictive Relationships for Sediment Physical and Geoacoustic Properties Based on the Index of Impedance (IOI) for Siliciclastic and Carbonate Sediments Combined. Coefficient of determination (r2) is given for each regression.

Parameter Regression r2 Sound Speed Ratio = 1.164 - 0.3001(IOI) + 0.1253(IOI)2 0.97Attenuation (k) = -3.31 + 4.33 (IOI) - 1.138 (IOI)2 0.22Porosity (%) = 174.16 - 89.12(IOI) + 13.37 (IOI)2 0.99Density (g cm-3) = 1.02 + 1.21LN(IOI) 0.99Mean Grain Size (θ) = 17.9 - 6.0(IOI) 0.84Sand and Gravel (%) = -113.4 + 89.1(IOI) 0.81

CONCLUSIONS

The Index of Impedance (IOI) can be used to predict accurately sound speed, density, and porosity in seafloor sediments and, with a lesser degree of accuracy, predict mean grain size and percent sand and gravel. The lower values of the coefficient of determination (r2) between IOI and mean grain size (percent sand and gravel) compared to sediment bulk density, porosity, or sound speed reflect the lack of fundamental physical relationship between mean grain size and either sediment bulk

density or sound speed (Fig. 3). The coefficients of determination (r2) are 0.84 and 0.64, respectively. In muddy sediments, consolidation (dewatering) lowers porosity and increases density without a change in mean grain size. In sands, porosity can vary up to 10%, depending on packing [7]. Given the same packing a uniform assemblage of spheres would theoretically achieve the same porosity regardless of grain diameter (size). Using values of mean grain size as an index, especially in the silt-size range, may be very misleading because of major differences in sorting (standard deviation of the particle size distribution). Well-sorted sediment composed of wholly silt-size particles may have the same mean grain size as poorly sorted sediment with a mixture of sand- and clay-size particles. The resultant density and sound speed of these two sediments, however, might be very different. Given the aforementioned issues, it is perhaps amazing that empirical regressions between grain size-related parameters and sediment density, porosity, sound speed, or impedance have any predictive value.

FIGURE 3. Scatter diagrams of mean grain size versus porosity and sound speed (Vp). The lighter colored symbols, which represent carbonate sediments, overlay the darker colored symbols, which represent siliciclastic sediment. Mean grain sizes less than 4 phi are in the sand grain size, 4-8 phi are silt sized particles and greater than 8 phi are clay-sized particles.

The use of different empirical IOI regressions for carbonate sediments than for

siliciclastic sediments may be justified for some specific carbonate sites where intra-particulate porosity is high [2] but is not justified for more generalized relationships for all coastal sediments, based on the data presented here. Therefore, the regressions based on the combined data set (Table 5) are recommended for general use. The regressions presented by Richardson and Briggs [1] in 1993 do not significantly differ from those regressions developed from the much larger data sets from siliciclastic sediments used here (Tables 4 and 5). Mean absolute differences between the 1993 and 2004 IOI regressions were as follows: 1.4% for porosity, 0.0108 g cm-3 for bulk density, 0.13 phi for mean grain size, 0.0025 for velocity ratio and 3.8 m s-1 for sound speed. A regression between IOI and percent sand and gravel was not calculated by

Richardson and Briggs [1]. Attempts to predict compressional wave attenuation from IOI at these high acoustic frequencies (400 kHz) have failed because of the high, but unknown, contribution of scattering to the overall measured attenuation. Intrinsic attenuation probably does not exceed the lower level of the curvilinear fits given in Figures 1 and 2. However, it is notable that attenuation in the carbonate sediments is on average 0.14 dB m-1 kHz-1 (56 dB m-1 @ 400 kHz) higher than for siliciclastic sediments.

Poro-elastic models predict that sound speed is dispersive, especially in sandy sediments [6]. The empirical relationships presented here were developed using sound speeds measured at 400 kHz. Typical echo sounders operate at 3.5 to 30 kHz, where sound speeds and thus impedance values may be lower. This dispersion effect is more pronounced in sand compared to muddy sediments. In the example given by Williams et al [7] for the sand sediment of the SAX99 experiments, measured sound speeds were 25-75 m/s higher at 400 kHz than over the 3.5- to 30-kHz frequency band. The calculated values of IOI, given the mean sediment density of 2.066 g cm-3, would be 2.4 g cm-3 at 400 kHz and 2.3 g cm-3 at 3.5 kHz. Based on this amount of sound speed dispersion, sediment properties predicted at 3.5 kHz would be different than from measured sound speeds (400 kHz): porosity is 2.6% higher, bulk density is 0.05 g/cm3 lower, mean grain size is 0.69 phi units higher (finer), and sound speed is 44 m/s higher.

ACKNOWLEDGMENTS

We acknowledge the considerable help of Richard I. Ray, the NORDA/NRL diving officer, who has been our indispensable diving companion for the past 20 years. The data summarized in this paper was collected over the past 25 years with financial support of the Office of Naval Research, Naval Research Laboratory, and the SACLANT Undersea Research Centre. This paper is NRL contribution number NRL/PP/7430-04-6.

REFERENCES

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2. Richardson, M.D., Lavoie, D.M. and Briggs, K.B. 1997. �Geoacoustic and physical properties of carbonate sediments of the Lower Florida Keys�, Geo-Marine Letters 17:316-324 (1997).

3. Richardson, M.D. and Briggs, K.B. �In-situ and laboratory geoacoustic measurements in soft mud and hard-packed sand sediments: Implications for high-frequency acoustic propagation and scattering.� Geo-Marine Letters 16:196-203 (1996).

4. Hamilton, E.L. �Prediction of in-situ acoustic and elastic properties of marine sediments�, Geophysics 36:266-289 (1971).

5. Richardson, M.D., Briggs, K.B., Bentley, S.J. Walter, D.J. and T.H. Orsi, T.H. �The effects of biological and hydrodynamic processes on physical and acoustic properties of sediments off the Eel River, California. Marine Geology 182:121-139 (2002).

6. Stoll, R.D. �Velocity dispersion in water-saturated granular sediment� Journal Acoustical Society of America 111(2):785-793 (2002).

7. Williams, K.L.., Jackson D.R., Thorsos, E.L., Tang, D. and Schock S.G. �Comparison of sound speed and attenuation measured in a sandy sediment to predictions based on Biot theory of porous media� IEEE Journal of Oceanic Engineering 27(3):413-428 (2002).